Under ideal conditions some common bacteria can divide and double their numbers in less than one half hour. Suppose one spring day at 6am a few such bacteria fall into a can of strawberry surup in a broken garbage bag behind a snack bar. These conditions-warmth, moisture, and lots of food - are perfect growth, and the population doubles every 20 minutes. By 6pm the bacteria overcrowds and dry the food and is gone. At what time did the can of syurup become half full?

Question

Advanced Placement (AP)

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1 August, 21:27

Under ideal conditions some common bacteria can divide and double their numbers in less than one half hour. Suppose one spring day at 6am a few such bacteria fall into a can of strawberry surup in a broken garbage bag behind a snack bar. These conditions-warmth, moisture, and lots of food - are perfect growth, and the population doubles every 20 minutes. By 6pm the bacteria overcrowds and dry the food and is gone. At what time did the can of syurup become half full?

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Randy Morton · Answer 1

Below is the solution:

If the population doubles every 20 minutes, and the can is full at 6:00PM, then the can must have been half full 20 minutes before 6:00PM or 5:40PM

Likewise the can is:

Full at 6:00PM

Half full at 6:00-0:20 = 5:40PM

1/4 full at 5:40 - 0:20 = 5:20PM

1/8 full at 5:20 - 0:20 = 5:00PM

1/16 full at 5:00 - 0:20 = 4:40PM